Individual Condensation Trails in Aircraft Trajectory Optimization

© Judith Rosenow

Contrails are formed by condensation of atmospheric water vapor on hydrophilic emissions (e.g. soot particles) from the engines. To ensure that the emitted (engine) heat does not prevent condensation, the atmosphere must be very cold. The critical temperature T_LM can be calculated using the Schmidt-Appleman criterion: If the straight mixing line intersects the curve of saturation vapor pressure e*, contrails are formed1.

© Judith Rosenow

This temperature criterion depends on the relative humidity U in the atmosphere and is also fulfilled in dry air from a cruising altitude of 10 km.

For contrails to develop into long-lasting cirrus clouds, the atmosphere must also be supersaturated with respect to ice. This happens in the atmosphere (near the tropopause) when there is sufficient water vapor available for natural cloud formation, but no natural condensation nuclei (e.g. salt crystals from seawater, desert sand or flower pollen). Our data analyses from modelled weather data in 2023 have shown a probability of ice supersaturation of 30 % to 50 % in the northern hemisphere.

© Judith Rosenow

In order to estimate the optical properties of contrails, both their microphysical properties and their lifetime must be determined. Our lifetime model1 calculates the mixing of the contrail with the atmosphere using a sheared Gaussian plume model.

© Judith Rosenow

The ice particle shapes depend on the temperature and the ice particle size increases as it grows into the ice-saturated air. The initial number of ice crystals is determined by the number of soot particles emitted. Subsequently, the crystals can fragment or clump together.

© Judith Rosenow

During its lifetime, the contrail is pushed in all directions by the wind. If it is not lifted upwards by the wind, the contrail falls downwards due to gravity. If the contrail leaves the ice-saturated layer or the ice water content falls below a critical value, the life of the contrail is over2.

© Judith Rosenow

This means that the lifespan is largely dependent on the size of the ice-saturated layer and the prevailing winds. Under typical vertical wind conditions, contrails live for several hours even in thin ice-saturated layers2.

Contrails act like a barrier in the Earth-atmosphere radiation balance. They scatter parts of the solar radiation back into the atmosphere (cooling effect). They also absorb and re-emit terrestrial radiation back to the Earth's surface (warming effect). The dominant effect can be determined using a Monte Carlo simulation1.

© Judith Rosenow

© Judith Rosenow

Due to the strong forward scattering, the optical properties depend not only on the size and number density of the ice crystals, but above all on the solar zenith angle and the intensity of the incoming radiation. The figure shows the radiation balance of contrails [W/(m2)] as a function of the position of the sun and the land use class. A cooling effect is therefore only likely at large solar zenith angles, e.g. during sunrise and sunset.

© Judith Rosenow

This angle varies in duration depending on the time of year and location. In the mid-latitudes between spring and fall, large angles occur for one to two hours during sunrise and sunset. In winter, large angles occur around midday for five consecutive hours.

• Judith Rosenow and Sophie Köhler (2024): Astronomical, Atmospheric, and Lifetime-specific Requirements for Cooling Contrails, Sesar Innovation Days 2024, Rome, Italy, https://doi.org/10.61009/SID.2024.1.09
• Judith Rosenow, Jakub Hospodka, Sébastian Lán, Hartmut Fricke, (2023): Validation of a Contrail Life-Cycle Model in Central Europe, Sustainability 15(11):8669, DOI:10.3390/su15118669
• Judith Rosenow, Hartmut Fricke and Lance Sherry, (2023): Time of the day-dependent impact of Contrail Avoidance Strategies on Airline Delay Costs, Fifteenth USA/Europe Air Traffic Management Research and Development Seminar (ATM2023), Savannah, Georgia
• Judith Rosenow and Hartmut Fricke, (2022): When do Contrails cool the Atmosphere? SESAR Innovation days 2022, Budapest, Hungary
• Gong Chen, Hartmut Fricke, Ostap Okhrin and Judith Rosenow, (2022), Importance of Weather Conditions in a Flight Corridor , Stats 2022, 5 (1), 312-338;https://doi.org/10.3390/stats5010018
• Judith Rosenow, Hartmut Fricke (2019):Condensation Trails in Trajectory OptimizationThirteenth USA/Europe Air Traffic Management Research and Development Seminar (ATM2019), 2019
• Judith Rosenow, Hartmut Fricke (2019):Individual Condensation Trails in Aircraft Trajectory Optimization, Sustainability, Volume 11, Issue 21, DOI: 10.3390/su11216082
• Judith Rosenow, Hartmut Fricke, Tanja Luchkova, Michael Schultz (2018): Minimizing contrail formation by rerouting around dynamic ice-supersaturated regions, Aeronautics and Aerospace Open Access Journal, Volume 2, Issue 3
• Judith Rosenow, Martin Lindner, Hartmut Fricke (2017): Impact of climate costs on airline network and trajectory optimization: a parametric study, CEAS Aeronautical Journal, Volume 8
• Judith Rosenow (2016):Optical Properties of Condensation Trails, Dissertation, Technische Universität Dresden

• Stanley Förster, Judith Rosenow, Martin Lindner and Hartmut Fricke (2016):  A toolchain for optimizing trajectories under real weather conditions and realistic flight performance , Greener Aviation, Brussels

• Judith Rosenow and Hartmut Fricke (2015): Angle dependent extinction of solar radiation by individual condensation trails, TAC-4 Proceedings, Bad Kohlgrub

• Michael Kaiser, Judith Rosenow, Hartmut Fricke and Michael Schultz (2012),

  Tradeoff between optimum altitude and contrail layer to ensure maximum ecological en-route performance using the enhanced trajectory prediction model (ETPM), Proceedings of the 2nd International Conference on Application and Theory of Automation in Command and Control Systems

• Judith Rosenow, Michael Kaiser and Hartmut Fricke (2012),

  Modeling Contrail life cycles based on highly precise flight profile data of modern aircraft, 5th International Conference on Research in Air Transportation, Berkely

• Judith Schiller, Michael Kaiser, Michael Schultz, Hartmut Fricke (2010), Impact of ocean currents on contrail formation on global scale, 9th Eurocontrol Innovative ATM Research Workshop, Bretigny, France

• MA (2023) 3D aircraft trajectory optimization with minimum contrail costs
• FP (2023) Bedingungen für kühlende Auswirkungen von Kondensstreifen im operationellen Betrieb
• DA (2024) Modellvergleich und Anwendbarkeitsanalyse globaler Klimamodelle für Luftfahrtemissionen
• DA (2019): Implementierung einer Berechnungsvorschrift für die Atmosphärische Turbulenz in eine Luftverkehrs-Simulationsumgebung
• FP (2019): Atmosphärische Turbulenz als Sicherheitsindikator in einer Luftverkehrs-Simulationsumgebung
• DA (2019): Untersuchung der globalen Verteilung des solaren Strahlungsspektrums
• FP (2019): Implementierung und Anwendung eines Strahlungstransfermodells zur Berechnung des orts- und zeitabhängigen Strahlungshaushaltes der Erde
• StA (2014): Modellierung der Rußemission moderner Strahltriebwerke zur Charakterisierung von Kondensstreifen